Computer Science > Computer Science and Game Theory

Title:Constructing Imperfect Recall Abstractions to Solve Large Extensive-Form Games

Abstract: Extensive-form games are an important model of finite sequential interaction
between players. The size of the extensive-form representation is, however,
often prohibitive and it is the most common cause preventing deployment of
game-theoretic solution concepts to real-world scenarios. The state-of-the-art
approach to solve this issue is the information abstraction methodology. The
majority of existing information abstraction approaches create abstracted games
where players remember all their actions and all the information they obtained
in the abstracted game -- a property denoted as a perfect recall. Remembering
all the actions, however, causes the number of decision points of the player
(and hence also the size of his strategy) to grow exponentially with the number
of actions taken in the past. On the other hand, relaxing the perfect recall
requirement (resulting in so-called imperfect recall abstractions) can
significantly increase the computational complexity of solving the resulting
abstracted game. In this work, we introduce two domain-independent algorithms
FPIRA and CFR+IRA which are able to start with an arbitrary imperfect recall
abstraction of the solved two-player zero-sum perfect recall extensive-form
game. The algorithms simultaneously solve the abstracted game, detect the
missing information causing problems and return it to the players. This process
is repeated until provable convergence to the desired approximation of the Nash
equilibrium of the original game. We experimentally demonstrate that even when
the algorithms start with trivial coarse imperfect recall abstraction, they are
capable of approximating Nash equilibrium of large games using abstraction with
as little as 0.9% of information sets of the original game.